WIAS Preprint No. 998, (2004)

Spatially adaptive regression estimation: Propagation-separation approach


  • Polzehl, Jörg
    ORCID: 0000-0001-7471-2658
  • Spokoiny, Vladimir
    ORCID: 0000-0002-2040-3427

2010 Mathematics Subject Classification

  • 62G05


  • adaptive weights; local structure, local polynomial regression, propagation, separation




Polzehl and Spokoiny (2000) introduced the adaptive weights smoothing (AWS) procedure in the context of image denoising. The procedure has some remarkable properties like preservation of edges and contrast, and (in some sense) optimal reduction of noise. The procedure is fully adaptive and dimension free. Simulations with artificial images show that AWS is superior to classical smoothing techniques especially when the underlying image function is discontinuous and can be well approximated by a piecewise constant function. However, the latter assumption can be rather restrictive for a number of potential applications. Here we present a new method based on the ideas of propagation and separation which extends the AWS procedure to the case of an arbitrary local linear parametric structure. We also establish some important results about properties of the new `propagation-separation' procedure including rate optimality in the pointwise and global sense. The performance of the procedure is illustrated by examples for local polynomial regression and by applications to artificial and real images.

Appeared in

  • Probab. Theory Related Fields, 135 (2006) pp. 335--362.

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